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A theoretical and numerical model for the study of incompressible mixture flows. (English) Zbl 1057.76060
Summary: We give a complete derivation of a new model for the study of incompressible mixture flows. The equations introduced are a generalization of a model previously studied in the literature [A. Onuki, J. Phys. Cond. Matter 9, 6119–6157 (1997)], in which the densities and the viscosities of the two phases are allowed to be different. Then, we introduce a finite difference scheme for numerical computations and qualitative validation of the model. In particular, the use of anti-diffusive second-order scheme for the transport scheme is explained and justified. One of the main physical experiment that we simulate is the spinodal decomposition under shear, but, in order to show that the model is relevant in many general situations, we also examine three other cases: the driven cavity, Rayleigh-Taylor instability and the fall of a droplet.

MSC:
76T10 Liquid-gas two-phase flows, bubbly flows
76M20 Finite difference methods applied to problems in fluid mechanics
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